In this paper we give a proposal for mirrors to (0,2) supersymmetric gauged linear sigma models (GLSMs), for those (0,2) GLSMs which are deformations of (2,2) GLSMs. Specifically, we propose a construction of (0,2) mirrors for (0,2) GLSMs with E terms that are linear and diagonal, reducing to both the Hori-Vafa prescription as well as a recent (2,2) nonabelian mirrors proposal on the (2,2) locus. For the special case of abelian (0,2) GLSMs, two of the authors have previously proposed a systematic construction, which is both simplified and generalized by the proposal here.

By studying the infra-red fixed point of an N = (0, 2) Landau-Ginzburg model, we find an example of modular invariant partition function beyond the ADE classification. This stems from the fact that a part of the left-moving sector is a new conformal field theory which is a variant of the parafermion model.

We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring of A/2-twisted twodimensional theories with (0,2) supersymmetry, quantum sheaf cohomology generalizes the notion of quantum cohomology. Complete descriptions of quantum sheaf cohomology have been obtained for abelian gauged linear sigma models (GLSMs) and for nonabelian GLSMs describing Grassmannians. In this paper we continue to explore the quantum sheaf cohomology of nonabelian theories. We first propose a method to compute the generating relations for (0,2) GLSMs with (2,2) locus. We apply this method to derive the quantum sheaf cohomology of products of Grassmannians and flag manifolds. The dual deformation associated with the biholomorphic duality gives rise to an explicit IR duality of two A/2-twisted (0,2) gauge theories.

We discuss the connections between the complex SYK model at the conformal limit and warped conformal field theories. Both theories have an SL(2 ,R)×U(1) global symmetry. We present comparisons on symmetries, correlation functions, the effective action and the entropy formula. We also use modular covariance to reinterpret results in the complex SYK model.

The study of Rényi mutual information (RMI) sheds light on the AdS/CFT correspondence beyond classical order. In this article, we study the Rényi mutual information between two intervals at large distance in two-dimensional holographic warped conformal field theory, which is conjectured to be dual to the gravity on AdS3 or warped AdS3 spacetime under the Dirichlet-Newman boundary conditions. By using the operator product expansion of twist operators up to level 3, we read the leading oder and the next-toleading order RMI in the large central charge and small cross-ratio limits. The leading order result is furthermore confirmed using the conformal block expansion. Finally, we match the next-to-leading result by a 1-loop calculation in the bulk.